Yes, I want to load just everything (ideally even when loading a savegame). Of course most "ideal" wish is to load even 3D models, but as Graf said, 3D models is low priority

Imho, for "loading just everything" better to add options to ingame menu (for example like current "precache gl textures" display option). This way we will have at least 2 benefits:
1) You can turn on/off this during a game without restarting gzdoom and/or modifying the mod
2) Mod will be playable for people with low amount of RAM (they just turn those precaches off)

Precaches are done on map load. For each savegame load, first the map needs to be loaded, so it should be precached as normal.
Regarding models, that's not going to be a quick fix, because the models exist somewhere outside the system. Refactoring the model subsystem to be better integrated is on the to-do list but not with the highest priority.

Precache GL textures option doesn't precache everything but only used textures and sprites.
For example, if you spawn an actor during gameplay and none of its class exists on the map initially, sprites for this actor won't be precached (without explicit precache entry in MAPINFO of course).
In other words, Precache GL textures won't help if you spawn most of actors dynamically.

My current problem is lags because of 3dmodels on Hi-end hardware. Example: https://www.youtube.com/watch?v=GY-xLSuhuWk (watch from start, and see the lag before door to minotaur is opened (at 0:01) ). This lag is because of supermap, located behind minotaur, is 3D model. My ACS workaround (see below) fixes this lag, but when savegame is loaded, it will lag (even with my workaround)

Taking into account what you said above I see that best solution for me is:
1) Make workaround with ACS script enter: spawnforced "actor with 3dmodel" on the first tic of each map (and thing_remove it on the second tic)
2) Wait for future fixes, when precacheactors will cache 3d models
3) Make several versions of the mod (one for low-end hardware, and one without lags)